Isoperimetric boundaries minimize area among regions enclosing a prescribed volume. Classical regularity theory implies that they are smooth away from a closed singular set of codimension at least seven; in particular, isolated singularities may occur in closed 8-manifolds. In this talk, I will discuss some examples of isoperimetric regions and present a generic regularity theorem: for a generic choice of metric and prescribed volume on a closed 8-dimensional manifold, every isoperimetric boundary is smooth and nondegenerate. Our approach is inspired by recent work of Li and Wang on generic regularity for singular minimal hypersurfaces. This is joint work with K. Marshall-Stevens and D. Parise.